Do I need to save the file so that I could edit my video sequence again?
Yes, you need to save your blend file through the file menu, then save. Blender has asked you to do so at least when you want to quit the program. When you didn't save that as well, your cutting work is lost and you have to start all over again...

The blend file contains all the sequences you put in the VSE. And the video footage itself needs to stay on your file system as well (at least relatively to your blend file, there are options to use no absolute paths).

So when you want to keep working on your cuts just open the blend file again and then switch to the VSE view if needed.

You will have everything explained in detail in the very helpful tutorial from Mikeycal Meyers on YouTube btw...